where \(\mathbb {V}(\hat{\mu }_i)\)  is the variance of this estimator
and \(\sigma _i^2\)  is the variance of population \(C_i\) .
We can estimate population mean \(\mu \)  by a weighted average over all \(\hat{\mu }_i\) s [1]}, i.e., 
\(\hat{\mu } = \sum _i \frac{|C_i|}{N} \cdot \hat{\mu }_i \qquad \textrm { with } \qquad \mathbb {V}(\hat{\mu }) = \sum _i \frac{(|C_i|)^2\cdot \sigma _i^2}{N^2\cdot n_i}.\) 
